Velocity and Magnetic Field Fluctuations in the Photosphere of a Sunspot

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Abstract
We use a data set of exceptionally high quality to measure oscillations of Doppler velocity, intensity, and the vector magnetic field at photospheric heights in a sunspot. Based on the full Stokes inversion of the line profiles of Fe I 630.15 and 630.25 nm, in the sunspot umbra we find upper limits of 4 G (root mean square [rms]) for the amplitude of 5 minute oscillations in magnetic field strength and 009 (rms) for the corresponding oscillations of the inclination of the magnetic field to the line of sight. Our measured magnitude of the oscillation in magnetic field strength is considerably lower than that found in 1997 by Horn, Staude, & Landgraf. Moreover, we find it likely that our measured magnetic field oscillation is at least partly due to instrumental and inversion cross talk between the velocity and magnetic signals, so that the actual magnetic field strength fluctuations are even weaker than 4 G. In support of this we show, on the basis of the eigenmodes of oscillation in a theoretical model of the sunspot umbra, that magnetic field variations of at most 0.5 G are all that is to be expected. The theoretical model also provides an explanation of the shift of power peaks in Doppler velocity to the 3 minute band in chromospheric umbral oscillations, as a natural consequence of the drastic change in character of the eigenmodes of oscillation between frequencies of about 4.5 and 5.0 mHz due to increased tunneling through the acoustic cutoff-frequency barrier. Using measurements of the phase of velocity oscillations above the acoustic cutoff frequency, we determine the relative velocity response height in the umbra of four different photospheric spectral lines from the phase differences between velocities in these lines, assuming that the oscillations propagate vertically at the local sound speed. In spacetime maps of fluctuations in continuum intensity, Doppler velocity, magnetic field strength, and field inclination, we see distinct features that migrate radially inward from the inner penumbra all the way to the center of the umbra, at speeds of a few tenths of a kilometer per second. These moving features are probably a signature of the convective interchange of magnetic flux tubes in the sunspot, although we failed to find any strong correlation among the features in the different quantities, indicating that these features have not been fully resolved.

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